# Quantum Physics: electron within the nucleus.

#### frankR

Calculate the smallest allowed energy of an electron were trapped inside an atomic nucleus of diameter 1.4x10^-14 meters. Compare this number with the several MeV of energy binding protons and neutrons inside the nucleus. On this basis, should we expect to find electrons within the nucleus?

I'm experiencing some confusion regarding what this statement is asking.

Do I assume that the question pertains to a one proton nucleus, under the Bohr model? However it states energies between protons and neutrons so the Bohr model must not pertain to the question.

I can find the electric potential of the electron if I know how many protons are contained within the nucleus. Do I use:

r = roA1/3 to find the number of protons?

Thereafter use U = k q1*q2/r to find the potential. Is this how this is done.

The correct answer should be 1900MeV.

Thanks

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#### arcnets

I think it has nothing to do with protons.

I think they just want you to use a 'potential well'. Meaning V(r) = 0 if r <= R, and V(r) = [oo] if r > R.

#### Tom Mattson

Staff Emeritus
Gold Member
Originally posted by frankR
Calculate the smallest allowed energy of an electron were trapped inside an atomic nucleus of diameter 1.4x10^-14 meters.
OK

Do I assume that the question pertains to a one proton nucleus, under the Bohr model? However it states energies between protons and neutrons so the Bohr model must not pertain to the question.
No, I think this is a simple exercise in using the Uncertainty Principle. You have a &Delta;x (the size of the nucleus). From that you can calculate a &Delta;p, which is the smallest allowed momentum. From that you can calculate the smallest allowed KE.

#### frankR

Tom: You're correct, I got 1995MeV.

"Quantum Physics: electron within the nucleus."

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